By "retrieve" I presume you mean "read" ?
If the other user has granted you at least reviewer permissions on that
folder, yes - they need to grant reveiewer permissions at the root mailbox
folder as well, so you can add this mailbox to your folder list, in the
advance properties of the Exchange service (or if the Exchange admin has
granted you full mailbox permissions). You can open up other users' folders
if you have permissions to do so.

If you mean "recall", no, and don't bother with message recall anyway as it
rarely works.